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A numerical scheme for the quantile hedging problem

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  • Cyril B'en'ezet
  • Jean-Franc{c}ois Chassagneux
  • Christoph Reisinger

Abstract

We consider the numerical approximation of the quantile hedging price in a non-linear market. In a Markovian framework, we propose a numerical method based on a Piecewise Constant Policy Timestepping (PCPT) scheme coupled with a monotone finite difference approximation. We prove the convergence of our algorithm combining BSDE arguments with the Barles & Jakobsen and Barles & Souganidis approaches for non-linear equations. In a numerical section, we illustrate the efficiency of our scheme by considering a financial example in a market with imperfections.

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  • Cyril B'en'ezet & Jean-Franc{c}ois Chassagneux & Christoph Reisinger, 2019. "A numerical scheme for the quantile hedging problem," Papers 1902.11228, arXiv.org.
    • Handle: RePEc:arx:papers:1902.11228
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    References listed on IDEAS

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    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. Roxana Dumitrescu & Romuald Elie & Wissal Sabbagh & Chao Zhou, 2017. "A new Mertens decomposition of $\mathscr{Y}^{g,\xi}$-submartingale systems. Application to BSDEs with weak constraints at stopping times," Papers 1708.05957, arXiv.org, revised May 2023.
    5. Bruno Bouchard & Jean-François Chassagneux & Géraldine Bouveret, 2016. "A backward dual representation for the quantile hedging of Bermudan options," Post-Print hal-01069270, HAL.
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    Cited by:

    1. Christelle Dleuna Nyoumbi & Antoine Tambue, 2023. "A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 1-34, January.
    2. Luisa I. Martínez-Merino & Diego Ponce & Justo Puerto, 2023. "Constraint relaxation for the discrete ordered median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 538-561, October.
    3. Géraldine Bouveret & Athena Picarelli, 2020. "A Level-Set Approach for Stochastic Optimal Control Problems Under Controlled-Loss Constraints," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 779-805, September.

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